Review of Hedging a Payable or a Receivable in
a Foreign Currency
I. Idea is to offset a short position with a long
position, or, offset a long position with a
short position.
Account Receivable
Account Payable
Profit
Profit
Spot rate
0
Spot rate
S($/j)
0
S($/j)
Long Position
Short
position
Rate at due
date
A. Hedge with Forward Position
Profit
Profit
Short Forward
Forward
rate
Forward
rate
Long
Forward
0
S($/j)
Hedged
position
Gain=(S-F) x FX amount
Future
due date
0
S($/j)
Hedged
position
Gain=(F-S) x FX amt.
At
due
date
I. B. Hedge with Money Market (MM) Instrument
1. Buying a MM security is a long position.
2. Borrow at MM rate is a short position.
Account Payable
a) Buy and hold the foreign currency.
b) How much to buy?
c) Borrow cost of FX in U.S. MM.
d) Pay liability with foreign MM instrument.
e) Cost is same as forward hedge if IRP holds.
Account Receivable
a) Borrow in foreign currency.
b) How much to borrow?
c) Invest loan proceeds in U.S. MM instrument.
d) Pay off loan with receivable.
e) Cost is same as forward hedge if IRP holds.
I. C. Hedge with Options
1. Buying a call is a long position.
2. Buying a put is a short position.
Account Payable
Account Receivable
Buy calls with X=forward rate
Buy puts with X=forward rate
Profit (at expiration)
Profit (at expiration)
Forward
rate
0
Receivable
Forward rate
S($/j)
0
S($/j)
Payable
Profit
Profit
Net position
Net position
S($/j)
S($/j)
I. C. Hedge with Options
3. Buying a call is a long position.
4. Buying a put is a short position.
Account Payable
Account Receivable
Buy calls with X=forward rate
Buy puts with X=forward rate
Profit (at expiration)
Profit (at expiration)
Forward
rate
0
Receivable
Forward rate
S($/j)
0
S($/j)
Payable
Profit
Profit
Net position
Net position
S($/j)
S($/j)
I.
D. Hedge with Swaps.
1. This is a sequence of long or short forward
positions.
2. Use with a known sequence of future FX
payables or future FX receivables.
II.
Example :
S($/€) = $1.25/€
i$ = 4%/ year,
C0 = $0.05/€
1- year Forward = $1.23/€
i€ = 5.7%/year
P0 = $0.08/€
Position: €1 Million payable due in one year, or
€1Million receivable due in one year.
A.Forward Hedge:
Payable
Buy €1M at $1.23/€
= $1,230,000
Receivable
Sell €1M at $1.23/€
= $1,230,000
Suppose in 1- year S($/€) = $ 1.27/€
Gain = (1.27 – 1.23)X106
= $40,000
Gain =(1.23−1.27)X106
= −$40,000
II.
B. Money Market (MM) Hedge.
1. Account Payable €1 Million.
PV = €1 M = €946,100
(1.057)
In $ = $1.25 × €946,100=$1,182625
€
a. Borrow $1,182,625 in U.S. @ 4%.
b. Purchase €946,100 and invest at 5.7%.
⇒ €1M in one year.
c. In one year pay $1,229,930 in U.S.
II.
2. Account Receivable €1 Million.
a. Borrow €946,100 in euroland.
b. Purchase €946,100× $1.25 = $1,182,625.
€
c. Invest $1,182,625 for one year at 4%=
$11,229,930 in one year.
d. In one year pay loan of €1 M with €1 M
receivable.
V.C. Options Hedge.
1. Account payable €1Millon due in one year.
Buy one-year calls on €1M with X= $1.23/€
Premium = $0.05 × €1,000,000=$50,000 .
€
Profit
1,180,000
$50,000
$1.18
0
$1.23
S ($ / €)
at exp iration
MaxGain = $1.23 × €1,000,000-$50,000=$1,180,000.
€
BreakevenSpot Rate = $1.23 − $0.05 − S ($/ €)=0
€
€
And S($/€)=$1.18/€.
VII.
C. Continued
2. Account Receivable €1Milion in one year
Buy puts on €1M with expiration in one year
with X=$1.23/€.
Pr emium = $0.08 × €1,000,000=$80,000.
€
$1.23
0
$1.31
-$80,000
Max loss = $80,000
Breakeven spot = S($/€) -$1.23/€=$0.08/€
S($/€)=$1.31/€
Max Gain =?
S ($ / €)
at exp iration